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1. Elementary Statistics
Chapter 1:
Introduction to
Statistics
1.2 Types of Data
1

2. Chapter 1:
Introduction to Statistics
1.1 Statistical and Critical Thinking
1.2 Types of Data
1.3 Collecting Sample Data
2
Chapter Objectives:
1. Demonstrate knowledge of statistical terms.
2. Differentiate between the two branches of statistics.
3. Identify types of data.
4. Identify the measurement level for each variable.
5. Identify the four basic sampling techniques.
6. Explain the difference between an observational and an experimental study.
7. Explain how statistics can be used and misused.

3. 1. Distinguish between Parameter and Statistic
2. Distinguish between qualitative and quantitative variables
3. Distinguish between discrete and continuous variables
4. Determine the level of measurement of a variable:
Nominal, Ordinal, Interval, Ratio
3
Section Objectives

4. A major use of statistics is to collect and use sample data to make conclusions
about populations.
1.2 Types of Data, Key Concept
Parameter & Statistic
Parameter
A numerical measurement describing some characteristic of a population
Statistic
A numerical measurement describing some characteristic of a sample (based on a
sample)
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5. 5
Example 1: Parameter or Statistic?
Statistic
Parameter
1. The percentage of all students on campus who have a job is 85%.
2. A sample of 200 students is obtained, and from this sample we find
that 83% have a job.
1. Parameter: It is a numerical summary of a population.
2. Statistic: It is a numerical summary based on a sample.

6. Quantitative Data & Categorical (Qualitative)Data
Quantitative (or numerical) data
 consists of numbers representing counts or measurements.
Example: The weights of supermodels
Example: The ages of respondents
Categorical (or qualitative or attribute) data
 consists of names or labels (not numbers that represent counts or measurements).
Example: The gender (male/female) of professional athletes
Example: Shirt numbers on professional athletes uniforms - substitutes for names
1.2 Types of Data
6

7. 1.2 Types of Data, Quantitative Data
Data
Qualitative
Categorical
Quantitative
Numerical,
Can be ranked
Discrete
Countable
5, 29, 8000, etc.
Continuous
Can be decimals
2.59, 312.1, etc.
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Discrete & Continuous types:
Discrete data
 result when the data values
are quantitative and the
number of values is finite, or
“countable.”
Example: The number of tosses of a
coin before getting tails
Continuous (numerical) data
 result from infinitely many
possible quantitative values,
where the collection of
values is not countable (takes
place in an interval).
Example: The lengths of distances
from 0 cm to 12 cm

8. 8
Example 2:
Discrete or Continuous?
Continuous
Discrete

9. Nominal level of measurement characterized by data that consist of names, labels, or
categories only, and the data cannot be arranged in some order (such as low to high).
Example: Survey responses of yes, no, and undecided
Ordinal level of measurement involves data that can be arranged in some order, but
differences (obtained by subtraction) between data values either cannot be determined or
are meaningless.
Example: Course grades A, B, C, D, or F
Interval level of measurement involves data that can be arranged in order, and the
differences between data values can be found and are meaningful. However, there is
no natural zero starting point at which none of the quantity is present. A value of
zero does not mean the absence of the quantity. Arithmetic operations such as addition
and subtraction can be performed on values of the variable.
Example: Years 1000, 2000, 1776, and 1492
Ratio level of measurement data can be arranged in order, differences can be found and
are meaningful, and there is a natural zero starting point (where zero indicates that none
of the quantity is present). Differences and ratios are both meaningful. Arithmetic
operations such as multiplication and division can be performed on the values of the
variable.
Example: Class times of 50 minutes and 100 minutes
1.2 Types of Data, Levels of Measurement:
Another way of classifying data: 4 levels of measurement: nominal, ordinal, interval, and ratio.
9
Nominal -
categories only
(Names)
Ordinal -
categories with
some order (
nominal, plus can be
ranked (order))
Interval -
differences but no
natural zero point
(Ordinal, plus
intervals are
consistent)
Ratio - differences
and a natural zero
point(Interval, plus
ratios are consistent,
true zero)

10. 1.2 Types of Data, Levels of Measurement:
Another way of classifying data: 4 levels of measurement: nominal, ordinal, interval, and ratio.
10
Nominal -
categories only
(Names)
Ordinal -
categories with
some order (
nominal, plus can be
ranked (order))
Interval -
differences but no
natural zero point
(Ordinal, plus
intervals are
consistent)
Ratio - differences
and a natural zero
point(Interval, plus
ratios are consistent,
true zero)
Nominal level of measurement characterized by data that consist of names, labels, or categories only,
and the data cannot be arranged in some order (such as low to high).
Example: Survey responses of yes, no, and undecided
Eye colors (blue, brown, black, other)
Political party (Democrat, republican, Independent, other)
Ordinal level of measurement involves data that can be arranged in some order, but differences
(obtained by subtraction) between data values either cannot be determined or are meaningless.
Examples: Ranks of colleges: Ranks can be first, second, third, and so on, which determines an ordering.
A school teacher assigns grades of A, B, C, D, or F (These grades can be arranged in order, but we can’t
determine difference between the grades.)
Interval level of measurement involves data that can be arranged in order, and the differences between
data values can be found and are meaningful. However, there is no natural zero starting point at
which none of the quantity is present. A value of zero does not mean the absence of the quantity.
Arithmetic operations such as addition and subtraction can be performed on values of the variable.
Examples: Body temperatures of 98.20 F and 98.60 F
Example: Years 1000, 2000, 1776, and 1492
Ratio level of measurement data can be arranged in order, differences can be found and are meaningful,
and there is a natural zero starting point (where zero indicates that none of the quantity is present).
Differences and ratios are both meaningful. Arithmetic operations such as multiplication and division
can be performed on the values of the variable.
Examples: Distances (in km) travelled by cars (0 km represents no distance travelled, and 400 km is
twice as far as 200 km.)
Prices of college textbooks ($0 does represent no cost, and a $100 book does cost twice as much as a $50
book.)

11. 1.2 Types of Data, Levels of Measurement:
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Example 3:
Determine the measurement level.
Variable Nominal Ordinal Interval Ratio Level
Hair Color Yes No Nominal
Zip Code Yes No Nominal
Letter Grade Yes Yes No Ordinal
ACT Score Yes Yes Yes No Interval
Height Yes Yes Yes Yes Ratio
Age Yes Yes Yes Yes Ratio
Temperature (F) Yes Yes Yes No Interval
Nominal -
categories only
(Names)
Ordinal - categories
with some order (
nominal, plus can be
ranked (order))
Interval -
differences but no
natural zero point
(Ordinal, plus intervals
are consistent)
Ratio - differences
and a natural zero
point(Interval, plus
ratios are consistent,
true zero)

12. 12
Example 4:
a. Sample: 1000 adults surveyed, Population: All adults
b. Statistic
c. Ratio
d. Discrete
In a survey of 1000 adults, subjects were asked how often they wash their
hands after using a public restroom; 74% of the respondents said
“always.”
a. Identify the sample and the population.
b. Is the value of 74% a statistic or Parameter?
c. What is its level of measurement?
d. Are the numbers of subjects discrete or Continuous?

13. 13
Example 5: Determine the measurement level.
Nominal
Ordinal
Interval
Ratio
Exit poles: Voters political affiliation: Democrats,
Republicans, etc.
Fast Food Service Time: The time intervals of drive-up
customers from ordering to receiving their order.
Movie Ratings: Rating a movie 4 stars on a scale of 5 stars.
Body Temperatures: Body Temperatures of several subjects.
Example 6: What’s wrong with the conclusion?
SSNs: A number of people report the last 4 digits of their SSNs, and the
average of those digits are calculated
The digits are not counts or measure of anything and as Nominal values, it
makes no sense to calculate their average.

14. 1.2 Types of Data, Quantitative Data (Time)
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Recorded Values and Boundaries
Variable Recorded Value Boundaries
Length 15 centimeters (cm)
Temperature 86 Fahrenheit (F)
Time 0.43 second (sec)
Mass 1.6 grams (g)
14.5-15.5 cm
85.5-86.5 F
0.425-0.435 sec
1.55-1.65 g

15. • Big data
 refers to data sets so large and so complex that their analysis is beyond the capabilities of
traditional software tools. Analysis of big data may require software simultaneously
running in parallel on many different computers.
• Data science
 involves applications of statistics, computer science, and software engineering, along with
some other relevant fields (such as sociology or finance).
• Missing Data
 A data value is missing completely at random if the likelihood of its being
missing is independent of its value or any of the other values in the data set. That
is, any data value is just as likely to be missing as any other data value.
• A data value is missing not at random if the missing value is related to the reason
that it is missing.
1.2 Types of Data,
Correcting for Missing Data
1. Delete Cases: One very common method for dealing with missing data is to delete all subjects having any
missing values.
2. Impute Missing Values: We “impute” missing data values when we substitute values for them. 15